"That number is said to be multiplied by another, which is (combined / summed / taken) as many times as there are units in the multiplier. "

Tartaglia was a mathematics teacher in Verona, and Venice. and Professor of Euclid in Brescia. The translation appeared in Euclide Megarense ... solo introduttore delle scientie mathematice, meaning Euclid of Megara ... only introducer of scientific mathematics.

Megara should have been Alexandria, a common mistake. The geometer, Euclid of Alexandria, lived c. 325-264 BCE. The philosopher, Euclid of Megara, lived c. 430-360 BCE.

The Title page of Tartaglia's edition of Euclid's Elements can be seen below.

A New Model of Multiplication via Euclid

ABOUT In 1968 at age 7 in Grade 2, Jonathan J. Crabtree noticed Euclid's definition of multiplication made no sense. Two added to itself three times is 8, not 6, as people have said for centuries. (HINT 2 added to itself once is 4.)
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Jonathan went on to explore hundreds of original source mathematics books & manuscripts spanning 16 languages. Euclid's definition of multiplication had been incorrectly translated into English in 1570 and was NEVER corrected!
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Jonathan's recent published paper and conference presentation titled, The Lost Logic of Elementary Mathematics reveals when why and how western mathematics education came to be filled with mis-truths, contradictions and inconsistencies.